I’ve been using 6.35 mm = 1/4 for the bit diameter when calibrating and in Easel to output gcode. I just measured my bit however and it’s closer to 6.25 mm. Am I measuring it wrong, or is the advertised 1/4" diameter of the bit just a nominal measurement?

The tool diameter you mentioned (0.250"/6.35mm) is the nominal size. The manufacturer has a range in which their tools are made that is considered acceptable deviation, because nothing is ever perfect. You may also notice that, as you use the tool, it wears down to a smaller cut diameter. You’d really only notice those differences if you were doing precision joinery, though.

The CNC mills we have at work measure their own tools, and they almost always come in 0.002-0.004" (0.05-0.10mm) undersized in diameter.